SOLUTION: Hi thank you for your time! Here is the problem I am working on. WIll you show me how you come up with your solutions? Thank you again so much for your time! The world consumpti

Question 481250: Hi thank you for your time! Here is the problem I am working on. WIll you show me how you come up with your solutions? Thank you again so much for your time!
The world consumption of oil in millions of barrels per day is given by
f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985)
a. According to this equation, what was the oil consumption in 1990?
b. Using this equation, the maximum oil consumption will occur in what year?
c. What is the maximum oil consumption?
d. Does this equation realistically describe oil in 2030? why or why not?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985)
a. According to this equation, what was the oil consumption in 1990?
1990 - 1985 = 5
set x = 5 and solve f(5)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(5)^2 + 2(5) + 58
f(5)=-0.1(25) + 10 + 58
f(5)= 65.5 million barrels
.
b. Using this equation, the maximum oil consumption will occur in what year?
It would be the vertex.
x = -b/(2a)
x = -2/(2(-0.1))
x = -2/(-0.2)
x = 10
year:
1985 + 10 = 1995
.
c. What is the maximum oil consumption?
set x = 10 solve for f(x)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(10)^2 + 2(10) + 58
f(5)=-0.1(100) + 20 + 58
f(5)= 68 million barrels
.
d. Does this equation realistically describe oil in 2030? why or why not?
2030-1985 = 45
set x = 45 solve for f(x)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(45)^2 + 2(45) + 58
f(5)=-0.1(2025) + 90 + 58
f(5)=-54.5 million barrels
answer: NO, because the result is negative
.

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